What is the chance?

You have fifty coins totaling $1.00. You drop one down an open drain while tossing the coins in your hand. What is the chance that you have lost a quarter?

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There are two ways you can have fifty coins totaling $1.00; two dimes, forty pennies, and eight nickels; or two dimes, forty-five pennies, two nickels, and one quarter. These arrangements are equally probable, so there is a one­ half chance you had a quarter to begin with. The probability that you then dropped that quarter from all the coins in your hand is one fiftieth. Therefore, the total probability that you lost a quarter is one half times one fiftieth, or one one-hundredth.

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